4. For the following research situations, identify the most appropriate statistical test from the options below that could be used to analyze your collected data. Hint: please pay careful attention to the nature of each variable provided. Ifyou feel that there is not enough information provided and additional information would indicate use of a particular test, please state the assumption you are making. (30 points total I 2 points each) A. One-sample t-test B. Two-sample t-test C. Paired t-test D. I don't know (use this for the following reasons: the research design is unclear; if a statistical test exists that could be used to answer this question, I don't think we have learned it yet this semester; or the test does not exist). a) A randomized trial is conducted to test the effectiveness of a new design of football helmet to prevent concussions. A coin is ipped, and subjects are given either a new helmet, or the old standard design. Are players with the new helmets less likely to get a concussion than players with the old helmets? b) Is the typical chromium consumption by men aged 19-50 years signicantly different than the Adequate Intake Level of 35 as promulgated by the Institute of Medicine? - One sample t-test c) Tufts has 10,000 students this semester with an average IQ of 125, while Harvard has 20,000 with an average IQ of 115. Which institution has more intelligent students based on IQ, Tufts or Harvard? d) J ay-Z did not attend graduate school, but he did raise the interesting hypothesis that the average person has 99 problems. How could you test that statistically? e) A random sample of people from the US are compared to a random sample of people from China. Which group has the higher prevalence of colorectal cancer? i) A sample of students is collected. The students' happiness levels are measured, and then the students are given a statistics exam. The happiness level of those exact same unique students is then tested again. Did the happiness level change? (Happiness is measured as a continuous variable using a validated \"happiness\" scale). h) j) k) 1) Consider the sample of students discussed in (f) of this question. A aw in the \"happiness\" scale was discovered and these data were categorized into \"happy\" vs. \"unhappy\". Did the happiness level of students change after their statistics quiz? How do circulating levels of the stress hormone cortisol differ between Red Sox and Yankees fans? Does proximity to a bus route predict whether a child in Hong Kong will be diagnosed with asthma by age 18, after adjusting for ozone exposure and parental smoking history? One hundred married couples are enrolled in a dietary study. Does mean whole milk consumption differ between partners? Do pomegranates grown under the USDA organic standards have higher levels of Vitamin C than those grown under conventiOnal methods? m) Does the average bottle of wine contain 750 mL? 11) On average, do apple orchards in Londonderry, NH produce the same number of apples as orchards in Stowe, MA? Would this response differ if we were contemplating the average number of Hpneycrjsp and Magqyn apples that were grown in the same orchard in Stowe, MA (2)? Pick two choices, one for each question. A random sample of professors and their teaching assistants were enrolled in a study to assess the impact of Zoom on self-reported stress levels. Are the stress levels signicantly different from each other (1)? Do you think that Rachel and her teaching assistant have stress levels that are signicantly different from each other (2)? Pick two choices, one for each